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Topological fields:

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Bibliographic Details
Main Author:	Więsław, Witold (Author)
Format:	Book
Language:	English
Published:	New York [u.a.] Dekker 1988
Edition:	1. print.
Series:	Pure and applied mathematics 119
Subjects:	Feld > Mathematik Topologischer Körper Topologie
Online Access:	Inhaltsverzeichnis
Physical Description:	VII, 309 S.
ISBN:	082477731X

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MARC


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adam_text	Contents PREFACE iii 1. DEFINITIONS AND EXAMPLES 1 1. Bases of Zero Neighborhoods 1 2. Examples of Topological Fields 7 3. The Lattice LT(K) of Ring Topologies for a Field K 16 4. Existence of Field Topologies on Infinite Fields 20 5. Locally Bounded and Locally Unbounded Topologies 25 6. Topological Fields and Geometry 33 Notes 35 2. FUNDAMENTAL PROPERTIES OF ABSOLUTE VALUED FIELDS 37 1. Artin Whaples Approximation Theorem, Hensel s Lemma 37 2. Description of Absolute Values of Some Fields 42 3. Topological Characterizations of Absolute Valued Fields 50 4. Algebraic Characterizations of Absolute Values 56 5. Extensions of Absolute Valued Fields 59 Notes 65 3. NORMED FIELDS AND THEIR PROPERTIES 67 1. Examples and Properties of Normed Fields 67 2. The Gelfand Mazur Theorem 70 3. Topological Characterizations of Normed Fields 74 4. Regular and Nonregular Norms on Fields 83 5. Norms on the Quotient Fields of Dedekind Domains 91 6. Examples of Fields Complete with Respect to Norms Inequivalent to Absolute Values 107 Notes 110 4. KRULL VALUATIONS 116 1. Fundamental Properties of Valuations 116 2. Independence Theorems 122 v vi Contents 3. Topological Characterization of Fields with Valuations 123 4. Extensions of Valuations 127 Notes 128 5. TOPOLOGIES OF TYPE V 130 1. Fundamental Properties 130 2. Characterization of Topologies of Type V 134 3. Minimal Locally Bounded Ring Topologies on Fields 138 4. Strictly Minimal Topological Fields 141 Notes 145 6. LOCALLY COMPACT TOPOLOGICAL FIELDS 148 1. Examples of Locally Compact Fields 148 2. Characterizations of Locally Compact Fields 151 Notes 158 7. INDEPENDENT TOPOLOGIES ON FIELDS 159 1. Examples of Independent Topologies 159 2. Some Results on Independent Field Topologies 162 3. Topologies Bounded by Suprema of V Topologies 167 Notes 171 8. FIELDS COMPLETE IN TWO INDEPENDENT TOPOLOGIES 172 1. The Absolute Value Case 172 2. The Valuation Case 180 Notes 182 9. LOCALLY BOUNDED RING TOPOLOGIES ON FIELDS 183 1. Several Generalizations of Valuations 183 2. Nakano s Valuations 186 3. Locally Bounded Ring Topologies on Some Classes of Fields 195 4. Topological Characterizations of R and I 208 Note 211 10. CONNECTED FIELDS OF ARBITRARY CHARACTERISTIC 213 Notes 220 11. RING TOPOLOGIES ON THE RATIONAL NUMBER FIELD 222 12. LINEAR FIELD AND RING TOPOLOGIES ON THE QUOTIENT FIELD OF ARITHMETICAL RINGS 227 13. LOCALLY UNBOUNDED TOPOLOGIES ON FIELDS 235 14. AN EXTENSION PROBLEM FOR TOPOLOGICAL FIELDS 241 15. OPEN PROBLEMS 251 Contents vii APPENDIX: UNE/VRl/Y ORDERED GROUPS 258 NOTATION 262 BIBLIOGRAPHY 263 AUTHOR INDEX 301 SUBJECT INDEX 3O7
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isbn	082477731X
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physical	VII, 309 S.
publishDate	1988
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publisher	Dekker
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spelling	Więsław, Witold Verfasser aut Topological fields Witold Wieş/law 1. print. New York [u.a.] Dekker 1988 VII, 309 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 119 Feld Mathematik (DE-588)4280861-3 gnd rswk-swf Topologischer Körper (DE-588)4242582-7 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Topologischer Körper (DE-588)4242582-7 s DE-604 Feld Mathematik (DE-588)4280861-3 s Topologie (DE-588)4060425-1 s 1\p DE-604 Pure and applied mathematics 119 (DE-604)BV000001885 119 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000555434&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Więsław, Witold Topological fields Pure and applied mathematics Feld Mathematik (DE-588)4280861-3 gnd Topologischer Körper (DE-588)4242582-7 gnd Topologie (DE-588)4060425-1 gnd
subject_GND	(DE-588)4280861-3 (DE-588)4242582-7 (DE-588)4060425-1
title	Topological fields
title_auth	Topological fields
title_exact_search	Topological fields
title_full	Topological fields Witold Wieş/law
title_fullStr	Topological fields Witold Wieş/law
title_full_unstemmed	Topological fields Witold Wieş/law
title_short	Topological fields
title_sort	topological fields
topic	Feld Mathematik (DE-588)4280861-3 gnd Topologischer Körper (DE-588)4242582-7 gnd Topologie (DE-588)4060425-1 gnd
topic_facet	Feld Mathematik Topologischer Körper Topologie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000555434&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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work_keys_str_mv	AT wiesławwitold topologicalfields

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